'Castle' is a term with a variety of meanings, and it's difficult, even among historians, to agree on one specific enough to be useful while still covering the wide array of buildings commonly described as 'castles' - what term can be accurately used to describe the all of the following: Bodiam, an elderly knight's retirement home, Krak des Chevaliers, a monastic order's bastion and last retreat, and Pontefract, a royal fortress designed to project power into the surrounding lands? What aspects of construction unite them as castles but excludes other medieval architecture? Many castles were not useful fortifications or intended as such, but others had no other function.

Broadly, we might define a castle as a large medieval building with aspects of fortification. Those aspects reflect the realities of medieval warfare: walls are high to make scaling difficult; towers and bastions on later examples tend to be rounded to avoid attackers unpicking key points of the structure; crenellations exist so defenders can use bows from a standing posture while being protected from incoming missiles, et cetera.

By the sixteenth century, however, realities had changed. It's not entirely accurate to say that the introduction of cannon made castles obsolete, but it is accurate to say they changed methods of fortification. High walls were discarded in place of lower, thicker walls that could withstand cannon-fire, and on later forts walls tend to slope quite noticeably to deflect shots rather than absorb their force - the same principle as angled armour on a tank; ravelins and projected bastions appear to make scaling these lower walls more difficult by intensifying the fire from attackers' flanks; crenellations are replaced with simple parapets.

This is the style of fortification generally found in areas fortified in stone by English colonists. In fact, some of the 'purest' examples of seventeenth- and eighteenth-century fortifications can be found in North America, since the builders did not have to incorporate the structures of older forts into their buildings. No-one was building 'castles' as we understand them by the time the modern US was settled, and so that wasn't what was built.

(as an amusing aside - most medieval English castles didn't see much siege in the medieval period, but they did see sieges in the English Civil Wars in the seventeenth century - most siege-damaged castles in England were damaged by cannon, not by catapult.)

What do you see as the difference between a "castle" and a "fort"?